MEKTEKDAS - 04 Frame Analysis
Transcript of MEKTEKDAS - 04 Frame Analysis
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Topic 4
Frame AnalysisMeriam & Kraige:
Chapter 4.6
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Fakutas Teknik Mesin dan DirgantaraInstitute Teknologi Bandung
MS2121 Mekanika Teknik DasarDr. M.A. Kariem © 2013
Analysis of Frames
• Frames and machines are structures with at least one multi-
force member. Frames are designed to support loads andare usually stationary. Machines contain moving parts and
are designed to transmit and modify forces.
• A free body diagram of the complete frame is used to
determine the external forces acting on the frame.
• Internal forces are determined by dismembering the frame
and creating free-body diagrams for each component.
• Forces between connected components are equal, have
the same line of action, and opposite sense.
• Forces on two force members have known lines of action
but unknown magnitude and sense.
• Forces on multi-force members have unknownmagnitude and line of action. They must be represented
with two unknown components.
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Frames Which Cease to be Rigid when Detached from Their
Supports
• Some frames may collapse if removed from theirsupports. Such frames can not be treated as rigid
bodies.
• A free-body diagram of the complete frame
indicates four unknown force components which
can not be determined from the three equilibriumconditions.
• The frame must be considered as two distinct, but
related, rigid bodies.
• With equal and opposite reactions at the contactpoint between members, the two free-body
diagrams indicate 6 unknown force components.
• Equilibrium requirements for the two rigid
bodies yield 6 independent equations.
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Fakutas Teknik Mesin dan DirgantaraInstitute Teknologi Bandung
MS2121 Mekanika Teknik DasarDr. M.A. Kariem © 2013
Sample Problem 6.4
Members ACE and BCD are
connected by a pin at C and by the
link DE . For the loading shown,determine the force in link DE and
the components of the force exerted
at C on member BCD.
SOLUTION:
• Create a free-body diagram for thecomplete frame and solve for the
support reactions.
• Define a free-body diagram for
member BCD. The force exerted by the
link DE has a known line of action butunknown magnitude. It is determined
by summing moments about C .
• With the force on the link DE known,
the sum of forces in the x and y
directions may be used to find theforce components at C .
• With member ACE as a free-body,
check the solution by summing
moments about A.
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Sample Problem 6.4
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SOLUTION:
• Create a free-body diagram for the completeframe and solve for the support reactions.
N4800 y y A F N480 y A
mm160mm100 N4800 B M A N300 B
x x A B F 0 N300 x A
07.28tan
150
801
Note:
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Fakutas Teknik Mesin dan DirgantaraInstitute Teknologi Bandung
MS2121 Mekanika Teknik DasarDr. M.A. Kariem © 2013
Sample Problem 6.4
• Define a free-body diagram for member
BCD. The force exerted by the link DE hasa known line of action but unknown
magnitude. It is determined by summing
moments about C .
N561
mm100 N480mm06 N300mm250sin0
DE
DE C
F
F M
C F DE N561
• Sum of forces in the x and y directions may be used to find the force
components at C .
N300cos N5610
N300cos0
x
DE x x
C
F C F
N795 xC
N480sin N5610
N480sin0
y
DE y y
C
F C F
N216 yC
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Fakutas Teknik Mesin dan DirgantaraInstitute Teknologi Bandung
MS2121 Mekanika Teknik DasarDr. M.A. Kariem © 2013
Sample Problem 6.4
• With member ACE as a free-body, check
the solution by summing moments about
A.
0mm220795mm100sin561mm300cos561
mm220mm100sinmm300cos
x DE DE A C F F M
(checks)
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Machines
• Machines are structures designed to
transmit and modify forces. Their mainpurpose is to transform input forces into
output forces.
• Given the magnitude of P , determine the
magnitude of Q.
• Create a free-body diagram of thecomplete machine, including the reaction
that the wire exerts.
• The machine is a nonrigid structure. Use
one of the components as a free-body.
• Taking moments about A,
P b
aQbQaP M A 0
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Sample problem 4.6
The frame supports the 400-kg load in themanner shown. Neglect the weights of the
members compared with the forces induced
by the load and compute the horizontal and
vertical components of all forces acting on
each of the members.
SOLUTION
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Solution
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Fakutas Teknik Mesin dan DirgantaraInstitute Teknologi Bandung
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Sample problem 4.7
Neglect the weight of the frame and compute the
forces acting on all of its members.
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Solution Sample Problem 4.7
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Draw FBD: Number of Unknown: 4
Number of Equations: 3
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Solution Sample Problem 4.7 (Cont’d)
G
D
E
50 lbE
D
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Solution Sample Problem 4.7 (Cont’d)
= 50 lb
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MS2121 Mekanika Teknik DasarDr. M.A. Kariem © 2013
Solution Sample Problem 4.7 (Cont’d)
= 100 lb
15 lb =
= -20 lb
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MS2121 Mekanika Teknik DasarDr. M.A. Kariem © 2013
Sample Problem 4.8
The machine shown is designed as an overload protection device which
releases the load when it exceeds a predetermined value T . A soft metalshear pin S is inserted in a hole in the lower half and is acted on by the upper
half. When the total force on the pin exceeds its strength, it will break. The
two halves then rotate about A under the action of the tensions in BD and CD,
as shown in the second sketch, and rollers E and F release the eye bolt.
Determine the maximum allowable tension T if the pin S will shear when the
total force on it is 800 N . Also compute the corresponding force on the hinge
pin A.
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Solution Sample Problem 4.8
Draw FBD:
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Solution Sample Problem 4.8 (Cont’d)
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Sample Problem 4.10
In the particular position shown, the excavator applies a 20-kN force parallel to the
ground. There are two hydraulic cylinders AC to control the arm OAB and a singlecylinder DE to control arm EBIF .
(a) Determine the force in the hydraulic cylinders AC and the pressure p AC against
their pistons, which have an effective diameter of 95 mm.
(b) Also determine the force in hydraulic cylinder DE and the pressure pDE against its
105-mm-diameter piston.
Neglect the weights of the members compared with the effects of the 20-kN force.
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a) Draw FBD:
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b) Draw FBD:
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